You have to be VERY careful in D&D, and really any RPG, when it comes to restricting someone entirely from being able to do something. Otherwise, you could wind up in a situation where you get stuck.
Again, you don't want a situation where Gale could get stuck in a burning building with no way of escape. Or maybe that's a bad example. Say, you implement a "He can't do it because he's too weak" approach. But then, later in the game, Gale is the only one alive, and the only way to save your whole party is if Gale is able to do something that is now restricted because he's got 8 Strength. Now you've backed yourself into a corner.
Always best to implement modifiers than restrictions.
So, for example, I might apply a situational modifier to a halfling trying to make a 10 foot jump versus a half orc trying to make the same jump. The halfling might have an Athletics of +6, and the half orc +3, but I'd make the DC 5 for the half orc and 15 for the halfling.
Why? Because the halfling is like 3 foot 5 and the half orc is like 6 foot five. The half orc can practically stretch out the entire distance and almost touch the other side without even jumping. So, for him with his longer legs, the jump isn't as much of a strain. The halfling, however, is physically shorter and has a much further distance to jump comparatively.
So, similarly, with the smashing doors down example, it would make more sense to use Athletics, as someone said, to provide people with more "door breaking knowledge" with an added bonus over those who know nothing about it. Then you'd see a significant chance different between Lae'zel smashing down a door versus Gale. Lae'zel might get a +5 while Gale would get like a -1. Then set the DC to 12 or 13 and see who opens that door faster - Gale who needs to roll a 13 or 14? or Lae'zel who needs to roll like a 7 or 8?
That's typically how a DM would handle something like this. Very rarely do you want to completely restrict.
